The invention relates to the field of waveguiding, and in particular to an all-dielectric coaxial waveguide.
In Equations 1-4, E and B denote the electric and magnetic fields, respectively, with Ez and Bz giving the respective field component along the z-axis, and ETEM and BTEM giving the respective field components for the TEM wave; ez is a unit vector along the z-axis; xcexc and ∈ are the permeability and permittivity, respectively, of the medium within which the EM wave travels; c is the speed of light; kz is the axial wave number; and xcfx89 is the angular frequency of the EM wave.
Waveguides are the backbone of modern optoelectronics and telecommunications systems. There are currently two major, and very distinct, types of waveguides (metallic and dielectric) that are employed in two separate regimes of the electromagnetic spectrum, e.g., optical and radio. For radio frequencies, it is the metallic coaxial cable that is of greatest prominence.
By enclosing a single conducting wire in a dielectric insulator and an outer conducting shell, an electrically shielded transmission circuit called coaxial cable is obtained. In a coaxial cable, the electromagnetic field propagates within the dielectric insulator, while the associated current flow is restricted to adjacent surfaces of the inner and outer conductors. As a result, coaxial cable has very low radiation losses and low susceptibility to external interference. Coaxial cables were originally developed for communications, and are used currently for broad band audio and video signals and for data transmission in computer networks.
The solutions to Maxwell""s equations in the coaxial cable configuration generally support transverse electric (TE) and transverse magnetic (TM) modes as well as a particular form, which is called the transverse electromagnetic (TEM) wave. In this solution, both the electric and magnetic fields are transverse to the propagation vector k.
Ez=Bz=0xe2x80x83xe2x80x83(1)
The transverse component of the electric field satisfies,                                                         (                                                ∇                  2                                ⁢                                  -                                                            ∂                      2                                                              ∂                                              z                        2                                                                                                        )                        xc3x97                                          E                →                            TEM                                =          0                ⁢                  
                ⁢                                            (                                                ∇                  2                                ⁢                                  -                                                            ∂                      2                                                              ∂                                              z                        2                                                                                                        )                        ·                                          E                →                            TEM                                =          0                                    (        2        )            
The magnetic field is given by,
{right arrow over (B)}TEM=xc2x1{square root over (xcexc∈)}ezx{right arrow over (E)}TEMxe2x80x83xe2x80x83(3)
As a result the axial wave number assumes the infinite medium value,                               k          z                =                              ω            c                    ⁢                                    μ              ⁢                              xe2x80x83                            ⁢              ϵ                                                          (        4        )            
which implies the absence of a cutoff value since all the values of k are real.
The TEM mode is unique in that it has radial symmetry in the electric-field distribution and a linear relationship between frequency and wave vector. This gives the TEM mode two exceptional properties. The radial symmetry implies that one need not worry about possible rotations of the polarization of the field after it passes through the waveguide. In addition, the linear relationship assures that a pulse of different frequencies will retain its shape as it propagates along the waveguide. The crucial disadvantage of a coaxial metallic waveguide is that it is useless at optical wavelengths because of heavy absorption losses in the metal. For this reason, optical waveguiding is restricted to the use of dielectric materials. However, because of the differences in boundary conditions of the electromagnetic fields at metal and dielectric surfaces, it has not been previously possible to recreate a TEM-like mode with all-dielectric materials.
Consequently, optical waveguiding is performed using the traditional index-guiding , i.e., total internal reflection, mechanism as exemplified by the silica and chalcogenide optical fibers. Such dielectric waveguides can achieve very low losses. Although the optical fiber has proven to be undeniably successful in many ways, it is nevertheless plagued by two fundamental problems. Because the fundamental mode in the fiber has an electric field with two-fold p-like symmetry, the polarization of light coming in one end of the fiber and the polarization coming out the other are generally completely different. This leads to significant problems when coupling into polarization dependent devices. In addition, because the guiding involves total internal reflection, it is not possible for light to travel in a fiber with a sharp bend whose radius of curvature is less than 3 mm without significant scattering losses. For light at optical wavelengths, this is a comparatively enormous radius, thus limiting the scale of possible miniaturization.
Recently, however, all-dielectric waveguides have been introduced that confine optical light by means of one-dimensional and two-dimensional photonic bandgaps. Although single-mode propagation is still two-fold p-like symmetric, these new designs have the potential advantage that light propagates mainly through the empty core of a hollow waveguide, thus minimizing effects associated with material non-linearities and absorption losses. Moreover, since confinement is provided by the presence of at least a partial photonic bandgap, this assures that light should be able to be transmitted around a bend with a smaller radius of curvature than for the optical fiber.
The invention provides an all-dielectric coaxial waveguide, which combines some of the best features of the metallic coaxial cable and the dielectric waveguides. The all-dielectric coaxial waveguide supports a fundamental mode that is very similar to the TEM mode of the metallic coaxial cable. It has a radially symmetric electric field distribution so that the polarization is maintained throughout propagation. It can be designed to be single-mode over a wide range of frequencies. In addition, the mode has a point of intrinsic zero dispersion around which a pulse can retain its shape during propagation, and this point of zero dispersion can be placed in the single-mode frequency window. Finally, the coaxial omniguide can be used to guide light around sharp bends whose radius of curvature can be as small as the wavelength of the light. This waveguide design is completely general and holds over a wide range of structural parameters, materials, and wavelengths. The coaxial waveguide of the invention represents the first successful attempt to bridge the disparate modal regimes of the metallic coaxial cable and the dielectric waveguides.
In accordance with an exemplary embodiment, the invention provides an all-dielectric coaxial waveguide comprising a dielectric core region; an annulus of dielectric material, surrounding the core region, in which electromagnetic radiation is confined; and an outer region of cylindrically coaxial dielectric shells of alternating indices of refraction surrounding the annulus. The core region and the outer region have an average index of refraction which is higher than the index of refraction of the annulus.
In general, in another aspect, the invention features an all-dielectric coaxial waveguide which supports a transverse electromagnetic wave that is similar to a TEM mode supported in a metallic coaxial cable. In yet another aspect, the invention features an all-dielectric coaxial wave guide having a fundamental electromagnetic wave guided mode that is axially symmetric, has predominantly radial electric field, and linear dispersion for a range of frequencies.